context-free parallel reduction on closures is confluent!

[helm.git] / matita / matita / contribs / lambda_delta / basic_2 / notation.ma

diff --git a/matita/matita/contribs/lambda_delta/basic_2/notation.ma b/matita/matita/contribs/lambda_delta/basic_2/notation.ma
index 509e6a7e891fb1a6315cb0c8b5f19d7e7d5cfa58..42f62ca150ece12d772be435e13308a9ec37bbc3 100644 (file)
--- a/matita/matita/contribs/lambda_delta/basic_2/notation.ma
+++ b/matita/matita/contribs/lambda_delta/basic_2/notation.ma
@@ -48,21 +48,45 @@ notation "hvbox( ② { I } break term 55 T1 . break term 55 T )"
  non associative with precedence 55
  for @{ 'SnItem2 $I $T1 $T }.
 
-notation "hvbox( ⓑ { I } break term 55 T1 . break term 55 T )"
+notation "hvbox( ⓑ { a , I } break term 55 T1 . break term 55 T )"
  non associative with precedence 55
- for @{ 'SnBind2 $I $T1 $T }.
+ for @{ 'SnBind2 $a $I $T1 $T }.
+
+notation "hvbox( + ⓑ { I } break term 55 T1 . break term 55 T )"
+ non associative with precedence 55
+ for @{ 'SnBind2Pos $I $T1 $T }.
+
+notation "hvbox( - ⓑ { I } break term 55 T1 . break term 55 T )"
+ non associative with precedence 55
+ for @{ 'SnBind2Neg $I $T1 $T }.
 
 notation "hvbox( ⓕ { I } break term 55 T1 . break term 55 T )"
  non associative with precedence 55
  for @{ 'SnFlat2 $I $T1 $T }.
 
-notation "hvbox( ⓓ  term 55 T1 . break term 55 T2 )"
+notation "hvbox( ⓓ { a } term 55 T1 . break term 55 T2 )"
+ non associative with precedence 55
+ for @{ 'SnAbbr $a $T1 $T2 }.
+
+notation "hvbox( + ⓓ term 55 T1 . break term 55 T2 )"
+ non associative with precedence 55
+ for @{ 'SnAbbrPos $T1 $T2 }.
+
+notation "hvbox( - ⓓ term 55 T1 . break term 55 T2 )"
+ non associative with precedence 55
+ for @{ 'SnAbbrNeg $T1 $T2 }.
+
+notation "hvbox( ⓛ { a } term 55 T1 . break term 55 T2 )"
  non associative with precedence 55
- for @{ 'SnAbbr $T1 $T2 }.
+ for @{ 'SnAbst $a $T1 $T2 }.
 
-notation "hvbox( ⓛ  term 55 T1 . break term 55 T2 )"
+notation "hvbox( + ⓛ term 55 T1 . break term 55 T2 )"
  non associative with precedence 55
- for @{ 'SnAbst $T1 $T2 }.
+ for @{ 'SnAbstPos $T1 $T2 }.
+
+notation "hvbox( - ⓛ term 55 T1 . break term 55 T2 )"
+ non associative with precedence 55
+ for @{ 'SnAbstNeg $T1 $T2 }.
 
 notation "hvbox( ⓐ  term 55 T1 . break term 55 T2 )"
  non associative with precedence 55
@@ -96,11 +120,11 @@ notation "hvbox( T . break ④ { I } break { T1 , break T2 , break T3 } )"
  non associative with precedence 50
  for @{ 'DxItem4 $T $I $T1 $T2 $T3 }.
 
-notation "hvbox( # [ x ] )"
+notation "hvbox( # { x } )"
  non associative with precedence 90
  for @{ 'Weight $x }.
 
-notation "hvbox( # [ x , break y ] )"
+notation "hvbox( # { x , break y } )"
  non associative with precedence 90
  for @{ 'Weight $x $y }.
 
@@ -118,18 +142,6 @@ notation "hvbox( T1 ≃ break term 46 T2 )"
 
 (* Substitution *************************************************************)
 
-notation "hvbox( L ⊢ break 𝐑 [ d , break e ] break ⦃ T ⦄ )"
-   non associative with precedence 45
-   for @{ 'Reducible $L $d $e $T }.
-
-notation "hvbox( L ⊢ break  𝐈 [ d , break e ] break ⦃ T ⦄ )"
-   non associative with precedence 45
-   for @{ 'NotReducible $L $d $e $T }.
-
-notation "hvbox( L ⊢ break 𝐍 [ d , break e ] break ⦃ T ⦄ )"
-   non associative with precedence 45
-   for @{ 'Normal $L $d $e $T }.
-
 notation "hvbox( ⇧ [ d , break e ] break term 46 T1 ≡ break term 46 T2 )"
    non associative with precedence 45
    for @{ 'RLift $d $e $T1 $T2 }.
@@ -160,7 +172,7 @@ notation "hvbox( L ⊢ break term 46 T1 break ▶ [ d , break e ] break term 46
 
 (* Unfold *******************************************************************)
 
-notation "hvbox( @ [ T1 ] break term 46 f ≡ break term 46 T2 )"
+notation "hvbox( @ ⦃ T1 , break f ⦄ ≡ break term 46 T2 )"
    non associative with precedence 45
    for @{ 'RAt $T1 $f $T2 }.
 
@@ -188,6 +200,14 @@ notation "hvbox( L ⊢ break term 46 T1 break ▶ ▶ * [ d , break e ] break te
    non associative with precedence 45
    for @{ 'PSubstStarAlt $L $T1 $d $e $T2 }.
 
+notation "hvbox( T1 break ⊢ ▶ * [ d , break e ] break term 46 T2 )"
+   non associative with precedence 45
+   for @{ 'PSubstStarSn $T1 $d $e $T2 }.
+
+notation "hvbox( T1 break ⊢ ▶ ▶ * [ d , break e ] break term 46 T2 )"
+   non associative with precedence 45
+   for @{ 'PSubstStarSnAlt $T1 $d $e $T2 }.
+
 notation "hvbox( ▼ * [ d , break e ] break term 46 T1 ≡ break term 46 T2 )"
    non associative with precedence 45
    for @{ 'TSubst $T1 $d $e $T2 }.
@@ -232,59 +252,53 @@ notation "hvbox( h ⊢ break term 46 L1 • ⊑ [ g ] break term 46 L2 )"
 
 (* Unwind *******************************************************************)
 
-notation "hvbox( ⦃ h , break L ⦄ ⊢ break term 46 T1 •* break [ g ] break term 46 T2 )"
+notation "hvbox( L1 ⊢ ⧫ * break term 46 T ≡ break term 46 L2 )"
    non associative with precedence 45
-   for @{ 'StaticTypeStar $h $g $L $T1 $T2 }.
+   for @{ 'Unwind $L1 $T $L2 }.
 
 (* Reducibility *************************************************************)
 
-notation "hvbox( 𝐑  ⦃ T ⦄ )"
-   non associative with precedence 45
-   for @{ 'Reducible $T }.
-
 notation "hvbox( L ⊢ break 𝐑 ⦃ T ⦄ )"
    non associative with precedence 45
    for @{ 'Reducible $L $T }.
 
-notation "hvbox( 𝐈  ⦃ T ⦄ )"
-   non associative with precedence 45
-   for @{ 'NotReducible $T }.
-
 notation "hvbox( L ⊢ break 𝐈 ⦃ T ⦄ )"
    non associative with precedence 45
    for @{ 'NotReducible $L $T }.
 
-notation "hvbox( 𝐍  ⦃ T ⦄ )"
-   non associative with precedence 45
-   for @{ 'Normal $T }.
-
 notation "hvbox( L ⊢ break 𝐍 ⦃ T ⦄ )"
    non associative with precedence 45
    for @{ 'Normal $L $T }.
 
-notation "hvbox( 𝐖𝐇𝐑 ⦃ T ⦄ )"
+(* this might be removed *)
+notation "hvbox( 𝐇𝐑 ⦃ T ⦄ )"
    non associative with precedence 45
-   for @{ 'WHdReducible $T }.
+   for @{ 'HdReducible $T }.
 
-notation "hvbox( L ⊢ break 𝐖𝐇𝐑  ⦃ T ⦄ )"
+(* this might be removed *)
+notation "hvbox( L ⊢ break 𝐇𝐑  ⦃ T ⦄ )"
    non associative with precedence 45
-   for @{ 'WHdReducible $L $T }.
+   for @{ 'HdReducible $L $T }.
 
-notation "hvbox( 𝐖𝐇𝐈  ⦃ T ⦄ )"
+(* this might be removed *)
+notation "hvbox( 𝐇𝐈  ⦃ T ⦄ )"
    non associative with precedence 45
-   for @{ 'NotWHdReducible $T }.
+   for @{ 'NotHdReducible $T }.
 
-notation "hvbox( L ⊢ break 𝐖𝐇𝐈 ⦃ T ⦄ )"
+(* this might be removed *)
+notation "hvbox( L ⊢ break 𝐇𝐈 ⦃ T ⦄ )"
    non associative with precedence 45
-   for @{ 'NotWHdReducible $L $T }.
+   for @{ 'NotHdReducible $L $T }.
 
-notation "hvbox( 𝐖𝐇𝐍 ⦃ T ⦄ )"
+(* this might be removed *)
+notation "hvbox( 𝐇𝐍 ⦃ T ⦄ )"
    non associative with precedence 45
-   for @{ 'WHdNormal $T }.
+   for @{ 'HdNormal $T }.
 
-notation "hvbox( L ⊢ break 𝐖𝐇𝐍 ⦃ T ⦄ )"
+(* this might be removed *)
+notation "hvbox( L ⊢ break 𝐇𝐍 ⦃ T ⦄ )"
    non associative with precedence 45
-   for @{ 'WHdNormal $L $T }.
+   for @{ 'HdNormal $L $T }.
 
 notation "hvbox( T1 ➡ break term 46 T2 )"
    non associative with precedence 45
@@ -294,9 +308,21 @@ notation "hvbox( L ⊢ break term 46 T1 ➡ break term 46 T2 )"
    non associative with precedence 45
    for @{ 'PRed $L $T1 $T2 }.
 
-notation "hvbox( L1 ⊢ ➡ break term 46 L2 )"
+notation "hvbox( ⦃ L1 ⦄ ➡ break ⦃ L2 ⦄ )"
    non associative with precedence 45
-   for @{ 'CPRed $L1 $L2 }.
+   for @{ 'FocalizedPRed $L1 $L2 }.
+
+notation "hvbox( ⦃ L1, break T1 ⦄ ➡ break ⦃ L2 , break T2 ⦄ )"
+   non associative with precedence 45
+   for @{ 'FocalizedPRed $L1 $T1 $L2 $T2 }.
+
+notation "hvbox( L ⊢ break ⦃ L1, break T1 ⦄ ➡ break ⦃ L2 , break T2 ⦄ )"
+   non associative with precedence 45
+   for @{ 'FocalizedPRed $L $L1 $T1 $L2 $T2 }.
+
+notation "hvbox( ⦃ L1 ⦄ ➡ ➡ break ⦃ L2 ⦄ )"
+   non associative with precedence 45
+   for @{ 'FocalizedPRedAlt $L1 $L2 }.
 
 notation "hvbox( ⦃ h , break L ⦄ ⊢ break term 46 T1 ➸ break [ g ] break term 46 T2 )"
    non associative with precedence 45
@@ -304,23 +330,27 @@ notation "hvbox( ⦃ h , break L ⦄ ⊢ break term 46 T1 ➸ break [ g ] break
 
 (* Computation **************************************************************)
 
-notation "hvbox( T1 ➡* break term 46 T2 )"
+notation "hvbox( T1 ➡ * break term 46 T2 )"
    non associative with precedence 45
    for @{ 'PRedStar $T1 $T2 }.
 
-notation "hvbox( L ⊢ break term 46 T1 ➡* break term 46 T2 )"
+notation "hvbox( L ⊢ break term 46 T1 ➡ * break term 46 T2 )"
    non associative with precedence 45
    for @{ 'PRedStar $L $T1 $T2 }.
 
-notation "hvbox( L1 ⊢ ➡* break term 46 L2 )"
+notation "hvbox( T1 ➡ ➡ * break term 46 T2 )"
    non associative with precedence 45
-   for @{ 'CPRedStar $L1 $L2 }.
+   for @{ 'PRedStarAlt $T1 $T2 }.
 
-notation "hvbox( L ⊢ break term 46 T1 ➡* break 𝐍 ⦃ T2 ⦄ )"
+notation "hvbox( ⦃ L1 ⦄ ➡ * ⦃ L2 ⦄ )"
+   non associative with precedence 45
+   for @{ 'FocalizedPRedStar $L1 $L2 }.
+
+notation "hvbox( L ⊢ break term 46 T1 ➡ * break 𝐍 ⦃ T2 ⦄ )"
    non associative with precedence 45
    for @{ 'PEval $L $T1 $T2 }.
 
-notation "hvbox( ⬊ * term 46 T  )"
+notation "hvbox( ⬊ * term 46 T )"
    non associative with precedence 45
    for @{ 'SN $T }.
 
@@ -354,9 +384,9 @@ notation "hvbox( L ⊢ break term 46 T1 ⬌ break term 46 T2 )"
    non associative with precedence 45
    for @{ 'PConv $L $T1 $T2 }.
 
-notation "hvbox( T1 ⊢ ⬌ break term 46 T2 )"
+notation "hvbox( ⦃ L1 ⦄ ⬌ ⦃ L2 ⦄ )"
    non associative with precedence 45
-   for @{ 'CPConv $T1 $T2 }.
+   for @{ 'FocalizedPConv $L1 $L2 }.
 
 (* Equivalence **************************************************************)
 
@@ -364,9 +394,13 @@ notation "hvbox( L ⊢ break term 46 T1 ⬌* break term 46 T2 )"
    non associative with precedence 45
    for @{ 'PConvStar $L $T1 $T2 }.
 
-notation "hvbox( T1 ⊢ ⬌* break term 46 T2 )"
+notation "hvbox( ⦃ L1 ⦄ ⬌ * ⦃ L2 ⦄ )"
+   non associative with precedence 45
+   for @{ 'FocalizedPConvStar $L1 $L2 }.
+
+notation "hvbox( L1 ⊢ ⬌* break term 46 L2 )"
    non associative with precedence 45
-   for @{ 'CPConvStar $T1 $T2 }.
+   for @{ 'CPConvStar $L1 $L2 }.
 
 (* Dynamic typing ***********************************************************)